The long term goal of this project is to develop the mathematical framework and the computer implementation for quantitatively analyzing brain morphology and characterizing the way it is affected by normal and diseased aging. The basis of this methodological framework is a shape transformation that adapts the morphology of one brain, which is treated as a template, to the morphology of the brain under analysis. This transformation quantifies global and local morphological characteristics of the brain under analysis, with respect to the template which serves as a measurement unit. Inter-subject and inter-population comparisons are performed by comparing the corresponding shape transformations. The first specific aim of this project is to develop and validate a geometry-based shape transformation methodology, utilizing anatomical features extracted from MR images. Special emphasis is given to the geometric analysis of the cortical sulci often demarcating the boundaries between different functional cortical regions, and to structural irregularities, such as ventricular expansion and brain atrophy, occurring with aging and brain diseases. The second specific aim is to develop and validate a framework for characterizing shape properties of brain structures, such as local tissue loss and shape abnormalities, utilizing the shape transformation above. Finally, the third specific aim of this project is to test the utility of these methodologies in brain imaging studies, by applying them to a longitudinal study of aging. The goal here is to localize subtle morphological changes occurring in the brain with aging, and to associate such morphological changes with concurrent or subsequent functional and cognitive changes, which might be predictors of Alzheimer's disease.